Mourinho rested a host of first-team regulars, including Cristiano Ronaldo, for the first leg of the fourth-round clash with the Segunda Division B club but his side still cruised to victory with France striker Karim Benzema scoring twice.
Madrid have been victims of cup upsets in recent years, most famously their 4-0 thrashing by Alcorcon in 2009, but a repeat never looked likely at El Collao.
Mourinho told www.realmadrid.com: "I enjoyed the match more than the result, as well as the team's attitude because it was a match in which it was complicated to motivate people.
"It wasn't easy to compete against a team that plays with such tremendous enthusiasm.
"We didn't play a top quality match, but it was impossible to do any better.
"We won and practically sealed the tie. Footballers that hadn't had many minutes on the pitch have played and I liked that.
"We won, did our part, we were professional and honoured the name Real Madrid."
Although the scoreline may have been emphatic, Mourinho was impressed by Alcoyano, adding: "We're two teams from different championships. They played with a lot of enjoyment, intensity and motivation.
"They began the match better than us and I think that it's a good team.
"I don't know their competition well but they have interesting players and I'm sure their manager is good. I hope they had a good time because we didn't come to joke around and we did our job. I wish them lots of luck."
Mourinho singled out teenage winger Jose Rodriguez for particular praise following his debut goal.
"I liked how he played, we all liked how he played," said the Portuguese.
"He has potential, youth and time to progress in order to play with the first team and not pass through the first team but arrive and stay. That's important.
"He has potential and the age to build a career here. If possible, by playing more because he doesn't play a lot at the moment and it's important for him to have more minutes on the field."